The present section contains the result of experiments and experience on points which, for the most part, are of interest only to those who study the scientific side of railway work. I here take the opportunity of placing on record various considerations, more or less connected with the subject of narrow-gauge railways, of too technical a nature to be mixed up with the descriptive pages. This explanation will account for the somewhat disjointed nature of the statements which follow.

The fact that narrow gauge locomotives are usually required to surmount much steeper gradients than are generally to be found on standard railways, makes adhesion a question of the first importance. It is very generally supposed that the co-efficient of adhesion between a wheel and a rail is a constant fraction of the insistent weight, varying slightly with the molecular structure of the metals in contact. There is, however, reason to believe that it decreases considerably with an increase of weight. In locomotives of the standard gauge, with from 12 to 18 tons per driven axle, it is generally held that a co-efficient of adhesion of one-sixth is all that can be counted on with certainty. From a number of experiments on the Festiniog Railway, with the results of which the late Mr. Spooner, who himself supported the theory, was good enough to supply me, I found that the load there per driven axle was five tons, the co-efficient averaging about one-fifth. Again, with my small engines that have a load on each axle of from 1.2 to 1.6 tons, the calculated co-efficient is two-ninths, in support of which I give the following experiment, conducted in the presence of two gentlemen belonging to a firm of locomotive builders, when it was under consideration to build for military purposes some engines on the plan of the No. 2 described in Section V.

I guaranteed that the locomotive referred to should take a load equal to its own weight up a gradient of 1 in 10 a quarter of a mile long, which then was, in parts, as steep as 1 in 9, with a short curve of half-a-chain radius at the severest part. This was satisfactorily accomplished. The day being dry, I was requested to ascertain what was the maximum load that could be hauled. On reaching four tons, when the start had to be made on a less gradient, the engine barely struggled up, and this was evidently all it could do. When full up with coal and water it weighed at that time 3 tons 6 cwt. During the experiment, however, there were but 3 tons 2 cwt. on the three axles, all of which were coupled. The boiler pressure was 145 lbs. exactly, and, the gross weight of engine and train being 7 tons 2 cwt., the gravity resistance on the gradient of 1 in 10 was equal to 14.2 cwt. The weight of 3 tons 2 cwt. available for adhesion, reduced by a tenth part, which the gradient converts into gravity resistance, was equal to 56 cwt. Thus, without reckoning the curve friction of the whole train and the journal friction of the wagons, both uncertain quantities, the proportion of developed tractive power to load was as 1 to 3.9. This result confirms the probability of the truth of the above assertion. Assuming its correctness, which appears beyond doubt, what is the explanation of increased proportionate adhesion with a decreased weight on the driven axles? The reduced diameter of wheel in the smaller engines might seem to offer a solution of the problem. Experience, however, goes to prove that, if there is any difference, a larger wheel has, with equal insistent weights, a better grip of the rail than a small one. I am of opinion that the weight is directly responsible for the difference. A wheel rests upon a rail on one point, or possibly on a transverse line of which the length is equal to the width of the rail. With a small insistent weight the molecules of the wheel and rail interlock without injury, and adhesion, on the principle of an infinitesimal rack and pinion, is the result. As the weight is increased on the fine bearing area, the molecules become disturbed, and fail to offer so firm a fulcrum. Ultimately they become displaced, and move as rollers between the two surfaces, materially reducing the adhesion. If this theory be the correct one, as is not improbable, the graduated reduction in the adhesion would be accounted for.

That the rolling wheel and rail do actually interlock was demonstrated by Sir Douglas Galton in his experiments on the retarding power of brakes, when he pointed out that, on a wheel becoming skidded, the rack and pinion motion was converted into a series of jumps of the wheel across the microscopic teeth of the rack, with a consequent reduction in adhesion proportionate to the sliding speed. In confirmation of this statement I detailed, during the meeting of the British Association at Sheffield, an experiment I made by reversing a locomotive so as to skid the wheels, and ultimately to cause them to revolve in a contrary direction, while descending an incline. With skidded wheels the descent was at a certain speed with backward revolution of the wheels the speed increased rapidly, the effect of the reversal being to cause the wheel to slip over the rail at a speed greater than that at which the engine was moving, thus showing that Sir Douglas Galton’s theory of the adhesion diminishing in proportion to the extent of departure from the interlocking or rolling motion of the wheel on the rail remained consistent even beyond sliding contact, and disposing of the old theory that the loss of adhesion with a skidded wheel was due to the creation of a polished point of contact on the wheel.

Another somewhat curious point in connection with adhesion is the slip of the driving wheels, which is naturally in the direction of causing a greater number of revolutions of the wheels than would be due to the length of rail travelled over. Occasionally, however, I have, in experimenting, noticed that fewer revolutions are made than would suffice to travel the distance as measured on a centre line between the rails. That is, the wheels slipped forward instead of back. This freak is probably due to the outer wheel on a curve slipping forward when, owing to considerable superelevation and a low speed, the inner wheel is the more heavily weighted, the distance then travelled being the reduced length of the inner rail.

I now proceed to explain the basis of calculation of the net loads hauled on various gradients, as appended to particulars of each locomotive described in Section V. The resistance on the level consists of journal friction, tire friction, and locomotive internal friction. Tire friction is practically nil, except on curves and in strong side winds. Journal friction I find, in the case of my small rolling stock, to be covered by an allowance of 10 lbs. per ton. Owing to the numerous curves another 10 lbs. per ton must be added to cover tire friction. A tractive power of 20 lbs. per ton proves quite sufficient to keep the train in motion on the level. It is not, however, enough to start the train on a curve, nor to overcome the inertia due to journal friction when, as on an incline, there is no slack between the wagons, and the whole train must be started at once. After considerable experience I find it necessary to add a further 20 lbs. per ton to the required tractive power. A total of 40 lbs. per ton is thus allowed as a good working equivalent of the frictional resistance of the train.

The friction of the locomotive is a much more complicated question. There seems very little information available on this point. It has been said, in the case of full sized engines, to absorb thirty per cent. of the tractive power, but this is a vague estimate, out of all reason excessive, unless it be intended to include gravity resistance on a steep incline. It is desirable to consider the nature of the various causes of resistance to motion separately. Viewed as a carriage only, the journal and tire friction of the locomotive may be taken at the same amount per ton of its weight as in the case of the trains, namely, 40 lbs. The additional resistance due to friction of the moving parts of the mechanism cannot be calculated as a constant. If the engine is developing but a small portion of its power, the amount will be small; when loaded to its full capacity there will be a large increase of internal resistance, varying, however, in proportion to the accuracy with which it is put together, and the stiffness of the framing.

Such experiments as I have made show clearly that, when exerting approximately its full power, the total frictional resistance of the engine does not exceed 100 lbs. per ton, and when running light is much less, but in what proportion less I have as yet failed to ascertain satisfactorily. Of this 100 lbs. per ton, from 20 to 40 lbs. is due to journal and tire friction, leaving from 60 lbs. to 80 lbs. per ton as the deduction for internal friction.

I thus conclude that an allowance of 40 lbs. per ton for train resistance, and 100 lbs. per ton for engine resistance, is a basis for calculating the tractive power required on the level that is sufficient under all possible narrow-gauge conditions. In the case of gradients there must, of course, be added the gravity resistance of the engine and train, which is, on a gradient of 1 in 100, one-100th of the gross weight; on a gradient of 1 in 50, one-50th, and so on.

In calculating the tractive power of the engine, the effective pressure in the cylinders may be reckoned at fully nine-tenths of the boiler pressure, on account of the low piston speed.

The above particulars are not to be taken as representative of what can be got out of a narrow-gauge engine in a few isolated experiments only, but of what is well within the compass of daily work.